FIA - NLS Models: Biomass Growth vs. Biomass, Temporally-balanced
JAH
2022-10-13
Background
This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the sum of tree biomass growth increment method for the plot biomass growth (\(G\)) calculation (see supplementary methods). Models are fitted separately by US ecoprovince
Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.
Data have increasing variance in \(G\) with increasing \(B\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}\) in equal-sample sized plot biomass bins (n=20) for each ecoprovince.
Model selection is used to determine. to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:
model 1: simple model \(G = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
model 2: phi model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
model 3: phi-alpha model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.
sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)
sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
NOTE:
This document contains a temporally balanced set of \(G\) observations. First, the data set limited to plots that meet our plot-based filtering criteria (see below). Then the data set was further restricted to plots with at least 2 \(G\) observations (i.e., three FIA tree census records), with one in each of the two following decades: 2000-2010 (including censuses part of FIA 3.0 from 1996-2000 as part of the 2000 panel), and 2011-2022. For plots that had >2 \(G\) observations we took the first and last ones.
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):
case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)
These data set cleaning criteria resulted in the exclusion of 1677 observations.
Below the model fitting procedure is implemented by ecoprovince:
Temporally-balancing the biomass growth data set
Lets look at some quick attributes of the dataset:
- The data set has 108135 observations, comprised of 56950 plots.
- The frequency of growth measurements among plots is as follows : 25737, 14117, 14220, 2876.
- Thus 54.81 % of plots have at least two growth intervals.
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4784 3418.7
## 2 4783 3416.0 1 2.645 3.703 0.05437 .
## 3 4782 3247.2 1 168.863 248.679 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 17365.95
## 2 2 17364.25
## 3 3 17123.56##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.131469 0.160885 0.817 0.414
## phi 0.006572 0.004971 1.322 0.186
## alpha 0.616728 0.036756 16.779 <2e-16 ***
## A 3.649488 0.116422 31.347 <2e-16 ***
## k 10.037803 0.836798 11.995 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.824 on 4782 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.59e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4782 3247.2
## 2 4781 3241.5 1 5.7127 8.4260 0.003716 **
## 3 4781 3241.9 0 0.0000
## 4 4780 3241.4 1 0.5820 0.8582 0.354289
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 17123.56
## 2 3a 17117.14
## 3 3b 17117.87
## 4 3c 17119.01##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.137026 0.161038 0.851 0.39487
## phi 0.006114 0.004963 1.232 0.21811
## alpha 0.614478 0.036736 16.727 < 2e-16 ***
## A 3.727638 0.125186 29.777 < 2e-16 ***
## k 16.050720 2.946710 5.447 5.38e-08 ***
## p 0.191531 0.056536 3.388 0.00071 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8234 on 4781 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 4.944e-07
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96731, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -14.161, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 178 rows containing non-finite values (stat_summary_bin).## Warning: Removed 178 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1256 row(s) containing missing values (geom_path).
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 11749 10574.1
## 2 11746 10532.7 3 41.39 15.388 5.469e-10 ***
## 3 11745 9879.3 1 653.45 776.861 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 41749.19
## 2 2 41699.80
## 3 3 40949.23##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.460005 0.143695 3.201 0.00137 **
## phi 0.027073 0.003893 6.954 3.75e-12 ***
## alpha 0.825898 0.027194 30.371 < 2e-16 ***
## A 2.990195 0.081105 36.868 < 2e-16 ***
## k 13.849194 0.647205 21.398 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9171 on 11745 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.043e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 11745 9879.3
## 2 11744 9778.5 1 100.817 121.082 < 2.2e-16 ***
## 3 11744 9804.4 0 0.000
## 4 11743 9777.6 1 26.841 32.236 1.398e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 40949.23
## 2 3a 40830.70
## 3 3b 40861.83
## 4 3c 40831.61##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.441431 0.141982 3.109 0.00188 **
## phi 0.027381 0.003866 7.082 1.5e-12 ***
## alpha 0.816236 0.027055 30.170 < 2e-16 ***
## A 3.243761 0.097183 33.378 < 2e-16 ***
## k 29.321917 2.662420 11.013 < 2e-16 ***
## p 0.196126 0.014537 13.491 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9125 on 11744 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 5.614e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 449 rows containing non-finite values (stat_summary_bin).## Warning: Removed 449 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1316 row(s) containing missing values (geom_path).
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5443 6161.6
## 2 5442 6160.8 1 0.807 0.7127 0.3986
## 3 5441 5911.9 1 248.898 229.0731 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 23135.70
## 2 2 23136.99
## 3 3 22914.40##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.443517 0.090979 -15.866 <2e-16 ***
## phi -0.006224 0.005391 -1.155 0.248
## alpha 0.680400 0.042432 16.035 <2e-16 ***
## A 6.575548 0.196248 33.506 <2e-16 ***
## k 22.072484 2.179249 10.128 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.042 on 5441 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.265e-06
## (8 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5441 5911.9
## 2 5440 5858.0 1 53.833 49.991 1.739e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 22914.40
## 2 3a 22866.58
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.473531 0.089253 -16.510 < 2e-16 ***
## phi -0.005956 0.005362 -1.111 0.26671
## alpha 0.679421 0.041892 16.218 < 2e-16 ***
## A 8.471464 0.599656 14.127 < 2e-16 ***
## k 135.622939 36.052377 3.762 0.00017 ***
## p 0.333113 0.022074 15.091 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.038 on 5440 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 5.561e-06
## (8 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 184 rows containing non-finite values (stat_summary_bin).## Warning: Removed 187 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1236 row(s) containing missing values (geom_path).
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3266 2821.2
## 2 3265 2817.2 1 3.96 4.5898 0.03224 *
## 3 3264 2607.6 1 209.68 262.4609 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 12271.84
## 2 2 12269.24
## 3 3 12018.42##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.100789 0.226876 -0.444 0.6569
## phi 0.020776 0.009551 2.175 0.0297 *
## alpha 0.832225 0.046720 17.813 <2e-16 ***
## A 4.708312 0.214756 21.924 <2e-16 ***
## k 31.488631 2.393785 13.154 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8938 on 3264 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.782e-06
## (5 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3264 2607.6
## 2 3263 2547.8 1 59.728 76.494 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 12018.42
## 2 3a 11944.66
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.133943 0.221239 -0.605 0.5449
## phi 0.018025 0.009345 1.929 0.0538 .
## alpha 0.824110 0.046217 17.831 < 2e-16 ***
## A 6.281777 0.438152 14.337 < 2e-16 ***
## k 112.639376 18.441855 6.108 1.13e-09 ***
## p 0.178895 0.012828 13.945 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8836 on 3263 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 9.181e-06
## (5 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92606, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -11.765, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 136 rows containing non-finite values (stat_summary_bin).## Warning: Removed 141 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1279 row(s) containing missing values (geom_path).
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6131 6669.8
## 2 6130 6658.8 1 11.004 10.13 0.001466 **
## 3 6129 6463.6 1 195.226 185.12 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24830.44
## 2 2 24822.31
## 3 3 24641.79##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.407158 0.093170 -15.10 < 2e-16 ***
## phi -0.022515 0.007102 -3.17 0.00153 **
## alpha 0.651389 0.045068 14.45 < 2e-16 ***
## A 7.147056 0.251328 28.44 < 2e-16 ***
## k 50.686599 3.984017 12.72 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.027 on 6129 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.344e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## model AIC
## 1 3 24641.79
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.407158 0.093170 -15.10 < 2e-16 ***
## phi -0.022515 0.007102 -3.17 0.00153 **
## alpha 0.651389 0.045068 14.45 < 2e-16 ***
## A 7.147056 0.251328 28.44 < 2e-16 ***
## k 50.686599 3.984017 12.72 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.027 on 6129 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.344e-06
## (2 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 228 rows containing non-finite values (stat_summary_bin).## Warning: Removed 228 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1298 row(s) containing missing values (geom_path).
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8164 24852
## 2 8163 24788 1 64.67 21.296 3.995e-06 ***
## 3 8162 23018 1 1769.84 627.581 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 45299.06
## 2 2 45279.79
## 3 3 44676.79##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.913956 0.101905 -8.969 < 2e-16 ***
## phi -0.033783 0.006375 -5.300 1.19e-07 ***
## alpha 0.904581 0.032985 27.424 < 2e-16 ***
## A 7.183336 0.188407 38.127 < 2e-16 ***
## k 4.264530 0.502079 8.494 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.679 on 8162 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.73e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8162 23018
## 2 8161 22955 1 62.655 22.2754 2.402e-06 ***
## 3 8161 22957 0 0.000
## 4 8160 22954 1 2.663 0.9466 0.3306
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 44676.79
## 2 3a 44656.53
## 3 3b 44657.03
## 4 3c 44658.09##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.926217 0.101199 -9.152 < 2e-16 ***
## phi -0.033728 0.006358 -5.305 1.16e-07 ***
## alpha 0.901351 0.032809 27.472 < 2e-16 ***
## A 7.423544 0.214506 34.608 < 2e-16 ***
## k 11.260249 2.763059 4.075 4.64e-05 ***
## p 0.337129 0.056220 5.997 2.10e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.677 on 8161 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.924e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 319 rows containing non-finite values (stat_summary_bin).## Warning: Removed 319 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1255 row(s) containing missing values (geom_path).
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7978 25296
## 2 7977 25249 1 46.28 14.622 0.0001324 ***
## 3 7976 23598 1 1651.45 558.183 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 43252.71
## 2 2 43240.09
## 3 3 42702.23##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.681866 0.128007 -5.327 1.03e-07 ***
## phi -0.034515 0.006578 -5.247 1.58e-07 ***
## alpha 0.888852 0.033928 26.198 < 2e-16 ***
## A 6.628775 0.215241 30.797 < 2e-16 ***
## k 11.166431 0.920464 12.131 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.72 on 7976 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.048e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7976 23598
## 2 7975 23443 1 155.023 52.737 4.173e-13 ***
## 3 7975 23484 0 0.000
## 4 7974 23440 1 43.892 14.931 0.0001124 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 42702.23
## 2 3a 42651.63
## 3 3b 42665.68
## 4 3c 42652.74##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.688250 0.126957 -5.421 6.10e-08 ***
## phi -0.034467 0.006538 -5.272 1.39e-07 ***
## alpha 0.879204 0.033729 26.067 < 2e-16 ***
## A 7.109710 0.263661 26.965 < 2e-16 ***
## k 27.822440 4.517425 6.159 7.68e-10 ***
## p 0.256828 0.028256 9.089 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.715 on 7975 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.537e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 312 rows containing non-finite values (stat_summary_bin).## Warning: Removed 312 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1239 row(s) containing missing values (geom_path).
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 828 2612.6
## 2 827 2612.6 1 0.013 0.0041 0.9489
## 3 826 2484.7 1 127.904 42.5193 1.218e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4460.386
## 2 2 4462.382
## 3 3 4422.670##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.460303 1.392394 1.049 0.29459
## phi -0.009615 0.029538 -0.326 0.74488
## alpha 0.866396 0.119147 7.272 8.25e-13 ***
## A 4.007083 0.896530 4.470 8.93e-06 ***
## k 12.599203 4.384869 2.873 0.00417 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.734 on 826 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.068e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_234, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_234, :
## parameters without starting value in 'data': p
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 826 2484.7
## 2 825 2470.1 1 14.651 4.8934 0.02723 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 4422.670
## 2 3a 4419.755
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.284095 1.306800 0.983 0.32608
## phi -0.006035 0.029574 -0.204 0.83836
## alpha 0.863186 0.119111 7.247 9.80e-13 ***
## A 4.476783 1.042824 4.293 1.97e-05 ***
## k 43.646726 33.869703 1.289 0.19788
## p 0.360039 0.119863 3.004 0.00275 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.73 on 825 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 7.67e-07
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.8582, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.819, p-value = 0.004817
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 33 rows containing non-finite values (stat_summary_bin).## Warning: Removed 33 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1212 row(s) containing missing values (geom_path).
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1260 1094.2
## 2 1259 1093.1 1 1.1063 1.2742 0.2591949
## 3 1258 1082.1 1 11.0489 12.8453 0.0003513 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4656.943
## 2 2 4657.665
## 3 3 4646.834##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.65627 0.30592 -2.145 0.032123 *
## phi 0.01046 0.01288 0.812 0.417208
## alpha 0.40995 0.10959 3.741 0.000192 ***
## A 4.19172 0.32018 13.092 < 2e-16 ***
## k 23.47473 4.02493 5.832 6.94e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9274 on 1258 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 4.683e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1258 1082.1
## 2 1256 1035.5 2 46.579 28.249 9.987e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 4646.834
## 2 3a NA
## 3 3b NA
## 4 3c 4595.262##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.70808 0.29077 -2.435 0.0150 *
## phi 0.01065 0.01258 0.847 0.3971
## alpha 0.43472 0.10329 4.209 2.75e-05 ***
## A 9.21966 12.33472 0.747 0.4549
## k 323.67972 599.31168 0.540 0.5892
## s 1.60302 0.94592 1.695 0.0904 .
## p 0.26034 0.36495 0.713 0.4758
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.908 on 1256 degrees of freedom
##
## Number of iterations to convergence: 14
## Achieved convergence tolerance: 9.084e-06
## (1 observation deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9178, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.508, p-value = 7.616e-11
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 48 rows containing non-finite values (stat_summary_bin).## Warning: Removed 48 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1306 row(s) containing missing values (geom_path).
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Error in nls(fg_1, data = G_255, start = c(ge = ge.start, A = A.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_255, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_255, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
262 - California Dry Steppe
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_263$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_263.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
322 - American Semidesert and Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
331 - Great Plains/Palouse Dry Steppe
model selection 1
## Error in nls(fg_1, data = G_331, start = c(ge = ge.start, A = A.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 104 285.83
## 2 103 277.64 1 8.1866 3.0371 0.08437 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 NA
## 2 2 379.8761
## 3 3 378.7376##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 11.4402 91.7591 0.125 0.9010
## phi 0.2633 0.1960 1.343 0.1822
## alpha 1.4472 0.7272 1.990 0.0492 *
## A 0.2025 1.1221 0.181 0.8571
## k 7.0363 12.0122 0.586 0.5593
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.642 on 103 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 8.911e-06summary
- simple model: does not fit
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_331, :
## parameters without starting value in 'data': s
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_331, :
## parameters without starting value in 'data': s
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 103 277.64
## 2 102 277.56 1 0.080696 0.0297 0.8636
## model AIC
## 1 3 378.7376
## 2 3a 380.7062
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 11.4402 91.7591 0.125 0.9010
## phi 0.2633 0.1960 1.343 0.1822
## alpha 1.4472 0.7272 1.990 0.0492 *
## A 0.2025 1.1221 0.181 0.8571
## k 7.0363 12.0122 0.586 0.5593
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.642 on 103 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 8.911e-06summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.88675, p-value = 1.502e-07
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.58007, p-value = 0.5619
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 4 rows containing non-finite values (stat_summary_bin).## Warning: Removed 4 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1366 row(s) containing missing values (geom_path).
plotting 2
332 - Great Plains Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 127 112.40
## 2 126 112.13 1 0.26844 0.3016 0.5838
## 3 125 109.08 1 3.04756 3.4922 0.0640 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 421.2904
## 2 2 422.9796
## 3 3 421.3975##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.2726 1.7336 0.157 0.8753
## A 4.1582 1.7879 2.326 0.0216 *
## k 101.1654 45.1400 2.241 0.0268 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9408 on 127 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.017e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 127 112.4
## 2 126 111.9 1 0.5007 0.5638 0.4541
## model AIC
## 1 1 421.2904
## 2 1a 422.7100
## 3 1b 423.2902
## 4 1c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.2726 1.7336 0.157 0.8753
## A 4.1582 1.7879 2.326 0.0216 *
## k 101.1654 45.1400 2.241 0.0268 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9408 on 127 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.017e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.87973, p-value = 7.476e-09
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.3275, p-value = 0.01994
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 4 rows containing non-finite values (stat_summary_bin).## Warning: Removed 4 rows containing missing values (geom_point).## Warning: Removed 2 rows containing missing values (geom_pointrange).## Warning: Removed 1288 row(s) containing missing values (geom_path).
plotting 2
341 - Intermountain Semi-desert & Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
342 - Intermountain Semi-Desert
model selection 1
## Error in nls(fg_1, data = G_342, start = c(ge = ge.start, A = A.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_342, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_342, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
411 - Everglades
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5077 3443.2
## 2 5076 3434.0 1 9.208 13.611 0.0002273 ***
## 3 5075 3214.7 1 219.349 346.286 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 18143.10
## 2 2 18131.50
## 3 3 17798.18##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.760791 0.197570 3.851 0.000119 ***
## phi 0.009542 0.004535 2.104 0.035417 *
## alpha 0.636808 0.031873 19.980 < 2e-16 ***
## A 2.977392 0.110237 27.009 < 2e-16 ***
## k 3.767706 0.519220 7.256 4.57e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7959 on 5075 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 2.728e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5075 3214.7
## 2 5074 3210.2 1 4.4803 7.0815 0.007813 **
## 3 5074 3213.0 0 0.0000
## 4 5073 3207.6 1 5.3515 8.4636 0.003639 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 17798.18
## 2 3a 17793.10
## 3 3b 17797.48
## 4 3c 17791.02##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.764045 0.197642 3.866 0.000112 ***
## phi 0.009677 0.004542 2.130 0.033180 *
## alpha 0.638591 0.031785 20.091 < 2e-16 ***
## A 2.920319 0.109849 26.585 < 2e-16 ***
## k 16.881030 3.542011 4.766 1.93e-06 ***
## p 0.553707 0.066927 8.273 < 2e-16 ***
## s 1.993079 0.535678 3.721 0.000201 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7952 on 5073 degrees of freedom
##
## Number of iterations to convergence: 14
## Achieved convergence tolerance: 7.509e-06summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 175 rows containing non-finite values (stat_summary_bin).## Warning: Removed 175 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1264 row(s) containing missing values (geom_path).
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5337 11963
## 2 5336 11916 1 47.468 21.256 4.111e-06 ***
## 3 5335 11670 1 245.864 112.397 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 26768.05
## 2 2 26748.82
## 3 3 26639.49##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.164602 0.124921 -9.323 < 2e-16 ***
## phi -0.035378 0.008384 -4.220 2.49e-05 ***
## alpha 0.793374 0.070937 11.184 < 2e-16 ***
## A 6.020186 0.221308 27.203 < 2e-16 ***
## k 11.354119 2.234415 5.081 3.87e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.479 on 5335 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.631e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 26639.49
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.164602 0.124921 -9.323 < 2e-16 ***
## phi -0.035378 0.008384 -4.220 2.49e-05 ***
## alpha 0.793374 0.070937 11.184 < 2e-16 ***
## A 6.020186 0.221308 27.203 < 2e-16 ***
## k 11.354119 2.234415 5.081 3.87e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.479 on 5335 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.631e-06summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 204 rows containing non-finite values (stat_summary_bin).## Warning: Removed 204 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1226 row(s) containing missing values (geom_path).
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 597 820.19
## 2 596 820.18 1 0.0117 0.0085 0.9267
## 3 595 797.12 1 23.0609 17.2136 3.827e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2462.209
## 2 2 2464.201
## 3 3 2449.089##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.17229 1.41660 1.533 0.1257
## phi -0.01169 0.03025 -0.386 0.6994
## alpha 0.87551 0.19632 4.460 9.82e-06 ***
## A 2.32697 0.49213 4.728 2.83e-06 ***
## k 19.88285 9.06806 2.193 0.0287 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.157 on 595 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 6.277e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 2449.089
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.17229 1.41660 1.533 0.1257
## phi -0.01169 0.03025 -0.386 0.6994
## alpha 0.87551 0.19632 4.460 9.82e-06 ***
## A 2.32697 0.49213 4.728 2.83e-06 ***
## k 19.88285 9.06806 2.193 0.0287 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.157 on 595 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 6.277e-06summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95126, p-value = 3.563e-13
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.084988, p-value = 0.9323
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 21 rows containing non-finite values (stat_summary_bin).## Warning: Removed 21 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1311 row(s) containing missing values (geom_path).
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 663 866.92
## 2 662 854.80 1 12.120 9.3866 0.002275 **
## 3 661 829.09 1 25.702 20.4908 7.107e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2729.245
## 2 2 2721.868
## 3 3 2703.536##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.10198 1.56501 1.343 0.17970
## phi 0.06479 0.02892 2.241 0.02539 *
## alpha 0.80384 0.16677 4.820 1.78e-06 ***
## A 2.13854 0.49961 4.280 2.14e-05 ***
## k 9.61180 3.71444 2.588 0.00987 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.12 on 661 degrees of freedom
##
## Number of iterations to convergence: 22
## Achieved convergence tolerance: 9.664e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M231, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 2703.536
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.10198 1.56501 1.343 0.17970
## phi 0.06479 0.02892 2.241 0.02539 *
## alpha 0.80384 0.16677 4.820 1.78e-06 ***
## A 2.13854 0.49961 4.280 2.14e-05 ***
## k 9.61180 3.71444 2.588 0.00987 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.12 on 661 degrees of freedom
##
## Number of iterations to convergence: 22
## Achieved convergence tolerance: 9.664e-06
## (2 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94157, p-value = 1.62e-15
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.1287, p-value = 2.917e-07
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 28 rows containing non-finite values (stat_summary_bin).## Warning: Removed 28 rows containing missing values (geom_point).## Warning: Removed 2 rows containing missing values (geom_pointrange).## Warning: Removed 1324 row(s) containing missing values (geom_path).
plotting 2
M242 - Cascade Mixed Forest
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 289 237.80
## 2 288 236.89 1 0.9123 1.1091 0.2932
## 3 287 218.47 1 18.4208 24.1990 1.466e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 824.5545
## 2 2 825.4321
## 3 3 803.7946##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.26208 1.70618 -0.154 0.87803
## phi 0.03132 0.03808 0.823 0.41143
## alpha 0.79043 0.14033 5.633 4.23e-08 ***
## A 2.55201 0.96322 2.649 0.00851 **
## k 35.96032 11.88470 3.026 0.00270 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8725 on 287 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.54e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 287 218.47
## 2 286 218.38 1 0.09401 0.1231 0.7259
## 3 286 218.47 0 0.00000
## 4 285 217.78 1 0.69081 0.9040 0.3425
## model AIC
## 1 3 803.7946
## 2 3a 805.6689
## 3 3b 805.7944
## 4 3c 806.8696##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.26208 1.70618 -0.154 0.87803
## phi 0.03132 0.03808 0.823 0.41143
## alpha 0.79043 0.14033 5.633 4.23e-08 ***
## A 2.55201 0.96322 2.649 0.00851 **
## k 35.96032 11.88470 3.026 0.00270 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8725 on 287 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.54e-06summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92069, p-value = 2.49e-11
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.3803, p-value = 0.1675
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 11 rows containing non-finite values (stat_summary_bin).## Warning: Removed 11 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1349 row(s) containing missing values (geom_path).
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 3a |
| 212 | Laurentian Mixed Forest | 3a |
| 221 | Eastern Broadleaf Forest | 3a |
| 222 | Midwest Broadleaf Forest | 3a |
| 223 | Central Interior Broadleaf Forest | 3 |
| 231 | Southeastern Mixed Forest | 3a |
| 232 | Outer Coastal Plain Mixed Forest | 3a |
| 234 | Lower Mississippi Riverine Forest | 3a |
| 242 | Pacific Lowland Mixed Forest | NA |
| 251 | Prairie Parkland (Temperate) | 3c |
| 255 | Prairie Parkland (Subtropical) | NA |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA |
| 313 | Colorado Plateau Semi-Desert | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | 3 |
| 332 | Great Plains Steppe | 1 |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | NA |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 3c |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 3 |
| M223 | Ozark Broadleaf Forest Meadow | 3 |
| M231 | Ouachita Mixed Forest | 3 |
| M242 | Cascade Mixed Forest | NA |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | NA |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA |
| M334 | Black Hills Coniferous Forest | 3 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.2.5 | ge.97.5 | phi | phi.2.5 | phi.97.5 | alpha | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 4788 | 2394 | 0.1370256 | -0.1786829 | 0.4527341 | 0.0061136 | -0.0036171 | 0.0158443 | 0.6144777 | 0.5424585 | 0.6864969 | 3.7276384 | 3.4822166 | 3.973060 | 16.050720 | 10.273812 | 21.82763 |
| 212 | Laurentian Mixed Forest | east | 11752 | 5876 | 0.4414314 | 0.1631222 | 0.7197406 | 0.0273810 | 0.0198026 | 0.0349595 | 0.8162358 | 0.7632041 | 0.8692675 | 3.2437614 | 3.0532673 | 3.434255 | 29.321917 | 24.103132 | 34.54070 |
| 221 | Eastern Broadleaf Forest | east | 5454 | 2727 | -1.4735313 | -1.6485025 | -1.2985600 | -0.0059560 | -0.0164676 | 0.0045556 | 0.6794207 | 0.5972956 | 0.7615457 | 8.4714639 | 7.2958986 | 9.647029 | 135.622939 | 64.945853 | 206.30002 |
| 222 | Midwest Broadleaf Forest | east | 3274 | 1637 | -0.1339434 | -0.5677252 | 0.2998385 | 0.0180249 | -0.0002985 | 0.0363483 | 0.8241103 | 0.7334938 | 0.9147267 | 6.2817773 | 5.4226971 | 7.140858 | 112.639376 | 76.480591 | 148.79816 |
| 223 | Central Interior Broadleaf Forest | east | 6136 | 3068 | -1.4071576 | -1.5898037 | -1.2245115 | -0.0225150 | -0.0364377 | -0.0085923 | 0.6513886 | 0.5630393 | 0.7397379 | 7.1470562 | 6.6543658 | 7.639747 | 50.686599 | 42.876527 | 58.49667 |
| 231 | Southeastern Mixed Forest | east | 8168 | 4084 | -0.9262167 | -1.1245924 | -0.7278410 | -0.0337276 | -0.0461909 | -0.0212642 | 0.9013512 | 0.8370363 | 0.9656661 | 7.4235438 | 7.0030571 | 7.844030 | 11.260249 | 5.843949 | 16.67655 |
| 232 | Outer Coastal Plain Mixed Forest | east | 7982 | 3991 | -0.6882500 | -0.9371198 | -0.4393803 | -0.0344671 | -0.0472838 | -0.0216504 | 0.8792035 | 0.8130865 | 0.9453206 | 7.1097098 | 6.5928656 | 7.626554 | 27.822440 | 18.967107 | 36.67777 |
| 234 | Lower Mississippi Riverine Forest | east | 832 | 416 | 1.2840954 | -1.2809489 | 3.8491397 | -0.0060349 | -0.0640838 | 0.0520140 | 0.8631864 | 0.6293909 | 1.0969818 | 4.4767829 | 2.4298818 | 6.523684 | 43.646726 | -22.834203 | 110.12766 |
| 242 | Pacific Lowland Mixed Forest | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 1264 | 632 | -0.7080765 | -1.2785284 | -0.1376246 | 0.0106532 | -0.0140195 | 0.0353260 | 0.4347183 | 0.2320868 | 0.6373498 | 9.2196578 | -14.9792587 | 33.418574 | 323.679719 | -852.082607 | 1499.44205 |
| 255 | Prairie Parkland (Subtropical) | pacific | 418 | 209 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 108 | 54 | 11.4402262 | -170.5423786 | 193.4228310 | 0.2632604 | -0.1255003 | 0.6520211 | 1.4472251 | 0.0049288 | 2.8895215 | 0.2025387 | -2.0228509 | 2.427928 | 7.036340 | -16.787042 | 30.85972 |
| 332 | Great Plains Steppe | interior west | 132 | 66 | 0.2725824 | -3.1578627 | 3.7030275 | NA | NA | NA | NA | NA | NA | 4.1581742 | 0.6202980 | 7.696051 | 101.165354 | 11.841451 | 190.48926 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 2 | 1 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 64 | 32 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 5080 | 2540 | 0.7640445 | 0.3765809 | 1.1515081 | 0.0096770 | 0.0007724 | 0.0185817 | 0.6385909 | 0.5762783 | 0.7009035 | 2.9203194 | 2.7049685 | 3.135670 | 16.881030 | 9.937159 | 23.82490 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 5340 | 2670 | -1.1646020 | -1.4094992 | -0.9197049 | -0.0353777 | -0.0518142 | -0.0189411 | 0.7933738 | 0.6543089 | 0.9324386 | 6.0201862 | 5.5863319 | 6.454040 | 11.354119 | 6.973753 | 15.73449 |
| M223 | Ozark Broadleaf Forest Meadow | east | 600 | 300 | 2.1722873 | -0.6098501 | 4.9544247 | -0.0116856 | -0.0710982 | 0.0477269 | 0.8755140 | 0.4899461 | 1.2610818 | 2.3269709 | 1.3604411 | 3.293501 | 19.882849 | 2.073551 | 37.69215 |
| M231 | Ouachita Mixed Forest | east | 668 | 334 | 2.1019804 | -0.9710094 | 5.1749702 | 0.0647916 | 0.0080089 | 0.1215742 | 0.8038450 | 0.4763735 | 1.1313164 | 2.1385430 | 1.1575385 | 3.119547 | 9.611801 | 2.318276 | 16.90533 |
| M242 | Cascade Mixed Forest | pacific | 40 | 20 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 12 | 6 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 20 | 10 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M334 | Black Hills Coniferous Forest | interior west | 292 | 146 | -0.2620761 | -3.6202910 | 3.0961387 | 0.0313211 | -0.0436238 | 0.1062660 | 0.7904348 | 0.5142206 | 1.0666490 | 2.5520107 | 0.6561375 | 4.447884 | 35.960321 | 12.568097 | 59.35255 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
plot ge
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
map2
## Warning: package 'ggnewscale' was built under R version 4.2.1## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
plot phi (effect of DeltaPDSI)
plot alpha (biomass growth compensation effect)
plot A (asymptote of forest biomass growth in Mg/ha/yr)
## Warning: Removed 20 rows containing missing values (geom_point).
plot k (stand biomass at half biomss G in Mg/ha)
## Warning: Removed 20 rows containing missing values (geom_point).
Caclulations - weighted averages
ge (stand biomass growth enhancement factor in % 2000-2021)
## region weighted.ge
## 1 entire US -0.3618113
## 2 pacific 0.0000000
## 3 east -0.3873071
## 4 interior west 2.1570380phi (effect of DeltaPDSI)
## region weighted.phi
## 1 entire US -0.005905188
## 2 pacific 0.000000000
## 3 east -0.006615666
## 4 interior west 0.067830119alpha (biomass growth compensation effect)
## region weighted.alpha
## 1 entire US 0.7611072
## 2 pacific 0.0000000
## 3 east 0.7674957
## 4 interior west 0.6987496A (asymptote of forest biomass growth in Mg/ha/yr)
## region weighted.A
## 1 entire US 5.614329
## 2 pacific 0.000000
## 3 east 5.686527
## 4 interior west 2.375343K (stand biomass at half biomss G in Mg/ha)
## region weighted.k
## 1 entire US 44.68927
## 2 pacific 0.00000
## 3 east 45.03369
## 4 interior west 44.42990